Local rigidity, contact homeomorphisms, and conformal factors

Institute for Mathematical Physics Rigidity for Local Holomorphic Conformal Embeddings from B Rigidity for Local Holomorphic Conformal Embeddings from B

In this article, we study local holomorphic conformal embeddings from B into B1 × · · · ×BNm with respect to the normalized Bergman metrics. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok and Mok-Ng. Applying holomorphic...

Conformal Quaternionic Contact Curvature and the Local Sphere Theorem

Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...

Geometric Rigidity of Conformal Matrices

We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace SO(n) by a arbitrary compact subset of conformal matrices, bounded away from 0 and invariant under SO(n), and rigid motions by Möbius transformations.

On Isometric and Conformal Rigidity of Submanifolds

Let f, g : Mn → Rn+d be two immersions of an n-dimensional differentiable manifold into Euclidean space. That g is conformal (isometric) to f means that the metrics induced on Mn by f and g are conformal (isometric). We say that f is conformally (isometrically) rigid if given any other conformal (isometric) immersion g there exists a conformal (isometric) diffeomorphism Υ from an open subset of...

Rigidity and Inflexibility in Conformal Dynamics